Fano fourfolds of K3 type

TL;DR

This paper identifies 64 families of Fano fourfolds of K3 type from a large database, analyzing their geometry and connections to known K3-related varieties, and exploring their invariants and rationality.

Contribution

It provides the first comprehensive list of Fano fourfolds of K3 type and investigates their geometric properties and origins, linking them to cubic fourfolds, Gushel-Mukai fourfolds, and K3 surfaces.

Findings

Produced a list of 64 Fano fourfold families of K3 type.

Analyzed their geometric properties and invariants.

Connected most to cubic fourfolds, Gushel-Mukai fourfolds, or K3 surfaces.

Abstract

We produce a list of 64 families of Fano fourfolds of K3 type, extracted from our database of at least 634 Fano fourfolds constructed as zero loci of general global sections of completely reducible homogeneous vector bundles on products of flag manifolds. We study the geometry of these Fano fourfolds in some detail, and we find the origin of their K3 structure by relating most of them either to cubic fourfolds, Gushel-Mukai fourfolds, or actual K3 surfaces. Their main invariants and some information on their rationality and on possible semiorthogonal decompositions for their derived categories are provided.